Question

Two families went to the Zoo. The Diaz family paid $170 for 3 children and 2 adults. The Jones family paid $360 for 4 children and 6 adults. If x is the price of a child’s ticket and y is the price of an adult’s ticket in dollars.
A. write a system of equations that models this situation.
B. How much does a child’s ticket cost?

Answer 1

Answer:

$\mathrm{A.\:}\begin{cases}3x+2y=170,\\4x+6y=360\end{cases}\\\\\mathrm{B.\:} \ 30$

Step-by-step explanation:

We can write the following system of equations:

$\begin{cases}3x+2y=170,\\4x+6y=360\end{cases}$, with variables as defined in the question.

Multiply the first equation by $-3$ and add both equations to isolate and solve for $x$:

$\begin{cases}-9x-6y=-510,\\4x+6y=360\end{cases}\\-5x=-150,\\x=\fbox{ \ 30 }$.